We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of...We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of G of size i, and yt（G） is the total domination number of G. In [7] We have obtained some properties of Dt（G, x） and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components. In this paper, we presented for any two isomorphic graphs the total domination polynomials are same, but the converse is not true. Also, we proved that for any n vertex transitive graph of order n and for any v ∈ V（G）, dt（G, i） = 7 dt（V）（G, i）, 1 〈 i 〈 n. And, for any k-regular graph of order n, dr（G, i） = （7）, i 〉 n-k and d,（G, n-k） = （kn） - n. We have calculated the total domination polynomial of Petersen graph D,（P, x） = 10X4 ＋ 72x5 ＋ 140x6 ＋ 110x7 ＋ 45x8 ＋ [ 0x9 ＋ x10. Also, for any two vertices u and v of a k-regular graph Hwith N（u） ≠ N（v） and if Dr（G, x） = Dt（ H, x ）, then G is also a k-regular graph.展开更多
A fully integrated CMOS bio-chip is designed in a SMIC 0.18μm CMOS mixed signal process and successfully integrated with a novel bio-nano-system. The proposed circuit integrates an array of 4 × 4 （16 pixels） o...A fully integrated CMOS bio-chip is designed in a SMIC 0.18μm CMOS mixed signal process and successfully integrated with a novel bio-nano-system. The proposed circuit integrates an array of 4 × 4 （16 pixels） of 19μm × 19μm electrodes,a counter electrode, a current mode preamplifier circuit （CMPA） ,a digital decoding circuit,and control logics on a single chip, It provides a - 1.6- 1.6V range of assembly voltage,Sbit potential resolution, and a current gain of 39.8dB with supply voltage of 1.8V. The offset and noise are smaller than 5.9nA and 25.3pArms,respectively. Experimental resuits from on-chip selective assembly of 30nm poly （ethylene glycol） （PEG） coated magnetic nano-particles （MNPs） targeted at biosensor applications are included and discussed to verify the feasibility of the proposed circuits.展开更多
文摘We have introduced the total domination polynomial for any simple non isolated graph G in [7] and is defined by Dt（G, x） = ∑in=yt（G） dr（G, i） x＇, where dr（G, i） is the cardinality of total dominating sets of G of size i, and yt（G） is the total domination number of G. In [7] We have obtained some properties of Dt（G, x） and its coefficients. Also, we have calculated the total domination polynomials of complete graph, complete bipartite graph, join of two graphs and a graph consisting of disjoint components. In this paper, we presented for any two isomorphic graphs the total domination polynomials are same, but the converse is not true. Also, we proved that for any n vertex transitive graph of order n and for any v ∈ V（G）, dt（G, i） = 7 dt（V）（G, i）, 1 〈 i 〈 n. And, for any k-regular graph of order n, dr（G, i） = （7）, i 〉 n-k and d,（G, n-k） = （kn） - n. We have calculated the total domination polynomial of Petersen graph D,（P, x） = 10X4 ＋ 72x5 ＋ 140x6 ＋ 110x7 ＋ 45x8 ＋ [ 0x9 ＋ x10. Also, for any two vertices u and v of a k-regular graph Hwith N（u） ≠ N（v） and if Dr（G, x） = Dt（ H, x ）, then G is also a k-regular graph.
文摘A fully integrated CMOS bio-chip is designed in a SMIC 0.18μm CMOS mixed signal process and successfully integrated with a novel bio-nano-system. The proposed circuit integrates an array of 4 × 4 （16 pixels） of 19μm × 19μm electrodes,a counter electrode, a current mode preamplifier circuit （CMPA） ,a digital decoding circuit,and control logics on a single chip, It provides a - 1.6- 1.6V range of assembly voltage,Sbit potential resolution, and a current gain of 39.8dB with supply voltage of 1.8V. The offset and noise are smaller than 5.9nA and 25.3pArms,respectively. Experimental resuits from on-chip selective assembly of 30nm poly （ethylene glycol） （PEG） coated magnetic nano-particles （MNPs） targeted at biosensor applications are included and discussed to verify the feasibility of the proposed circuits.
